Last week ThursdayThoughts showed a simple expression for the ratio of the gravitational force to the electromagnetic force between two electrons. This week's thought will present and discuss the solution.
Angle solution for stable and small collision angle:
φ = ArcTan(76172 ÷ 74445)
Collision angle = angle solution (above) - twist angle (quarter turn over 137 connections) - untwisted angle:
θ = φ - pi/274 - pi/4
θ = 8.087279825824565E-11 radians
|137||number of links|
|* (8.087280E-11)^2 / 2||est. one minus cos(θ)|
|/ 76172 / 74445||contact position|
|/ 11683264103||contact timing|
|/ 2||drag over 2|
|* 4 / 3 * 0.0072973525664^2||4/3 alpha squared|
|2.40053(11)E-43||vs. 2014 Codata derived|
The factor of 4/3 alpha squared was needed to balance to the experimental value. Alpha is also known as the electromagnetic coupling constant. It makes some sense that alpha squared is needed. I don’t know the source of the factor 4/3.
There are two advantages to this calculation. One is that the relationship is exact to the extent that alpha is known. This leads to a gravitational constant with the precision of alpha. The other is that it validates the process being used. This has far-reaching implications.
Next week ThursdayThoughts will explore possible sources of error in this calculation.